HP 15c Scientific Calculator User manual

HP-15C

Owner’s Handbook

HP Part Number: 00015-90001

Edition 2.4, Sep 2011

Legal Notice

This manual and any examples contained herein are provided “as is”

and are subject to change without notice. Hewlett-Packard Company

makes no warranty of any kind with regard to this manual, including,

but not limited to, the implied warranties of merchantability non-

infringement and fitness for a particular purpose. In this regard, HP

shall not be liable for technical or editorial errors or omissions

contained in the manual.

Hewlett-Packard Company shall not be liable for any errors or

incidental or consequential damages in connection with the furnishing,

performance, or use of this manual or the examples contained herein.

Reproduction, adaptation, or translation of this manual is prohibited

without prior written permission of Hewlett-Packard Company, except

as allowed under the copyright laws.

Hewlett-Packard Company

Palo Alto, CA

94304

USA

3

Introduction

Congratulations! Whether you are new to HP calculators or an experienced

user, you will find the HP-15C a powerful and valuable calculating tool.

The HP-15C provides:

 448 bytes of program memory (one or two bytes per instruction) and

sophisticated programming capability, including conditional and

unconditional branching, subroutines, flags, and editing.

 Four advanced mathematics capabilities: complex number calculations,

matrix calculations, solving for roots, and numerical integration.

 Direct and indirect storage in up to 67 registers.

This handbook is written for you, regardless of your level of expertise.

The beginning part covers all the basic functions of the HP-15C and how to

use them. The second part covers programming and is broken down into

three subsections  The Mechanics, Examples, and Further Information  in

order to make it easy for users with varying backgrounds to find the

information they need. The last part describes the four advanced

mathematics capabilities.

Before starting these sections, you may want to gain some operating and

programming experience on the HP-15C by working through the

introductory material, The HP-15C: A Problem Solver, on page 12.

The various appendices describe additional details of calculator operation,

as well as warranty and service information. The Function Summary and

Index and the Programming Summary and Index at the back of this manual

can be used for quick reference to each function key and as a handy page

reference to more comprehensive information inside the manual.

Also available from Hewlett-Packard is the HP-15C Advanced Functions

Handbook, which provides applications and technical descriptions for the

root-solving, integration, complex number, and matrix functions.

Note: You certainly do not need to read every part of the manual

before delving into the HP-15C Advanced Functions if you are

already familiar with HP calculators. The use of _ and f

requires a knowledge of HP-15C programming.

4

Contents

The HP-15C: A Problem Solver ....................................

12

A Quick Look at v .................................................

12

Manual Solutions ............................................................

13

Programmed Solutions .....................................................

14

Part I: HP-15C Fundamentals ................................

17

Section 1: Getting Started ..........................................

18

Power On and Off ..........................................................

18

Keyboard Operation .......................................................

18

Primary and Alternate Functions .....................................

18

Prefix Keys ..................................................................

19

Changing Signs ...........................................................

19

Keying in Exponents .....................................................

19

The "CLEAR" Keys ........................................................

20

Display Clearing: ` and − ...................................

21

Calculations ...................................................................

22

One-Number Functions .................................................

22

Two-Number Functions and v ...............................

22

Section 2: Numeric Functions .....................................

24

Pi ..................................................................................

24

Number Alteration Functions ............................................

24

One-Number Functions ....................................................

25

General Functions ........................................................

25

Trigonometric Operations ..............................................

26

Time and Angle Conversions .........................................

26

Degrees/Radians Conversions .......................................

27

Logarithmic Functions ...................................................

28

Hyperbolic Functions ....................................................

28

Two-Number Functions ....................................................

29

The Power Function ......................................................

29

Percentages .................................................................

29

Polar and Rectangular Coordinate Conversions ...............

30

Section 3: The Automatic Memory Stack, LAST X, and

Data Storage ........................................................

32

Contents 5

The Automatic Memory Stack and Stack Manipulation ........

32

Stack Manipulation Functions ........................................

33

The LAST X Register and K .......................................

35

Calculator Functions and the Stack .................................

36

Order of Entry and the v Key ...............................

37

Nested Calculations .....................................................

38

Arithmetic Calculations With Constants ...........................

39

Storage Register Operations ............................................

42

Storing and Recalling Numbers .....................................

42

Clearing Data Storage Registers ....................................

43

Storage and Recall Arithmetic ........................................

43

Overflow and Underflow ..............................................

45

Problems ........................................................................

45

Section 4: Statistics Functions .....................................

47

Probability Calculations ...................................................

47

Random Number Generator .............................................

48

Accumulating Statistics .....................................................

49

Correcting Accumulated Statistics ...................................

52

Mean ..........................................................................

53

Standard Deviation .......................................................

53

Linear Regression .........................................................

54

Linear Estimation and Correlation Coefficient ...................

55

Other Applications .......................................................

57

Section 5: The Display and Continuous Memory ...........

58

Display Control ..............................................................

58

Fixed Decimal Display ..................................................

58

Scientific Notation Display ............................................

59

Engineering Notation Display ........................................

59

Mantissa Display .........................................................

60

Round-Off Error ............................................................

60

Special Displays .............................................................

60

Annunciators ...............................................................

60

Digit Separators ...........................................................

61

Error Display ...............................................................

61

Overflow and Underflow ..............................................

61

Low-Power Indication ....................................................

62

Continuous Memory ........................................................

62

Status .........................................................................

62

6 Contents

Resetting Continuous Memory ........................................

63

Part II: HP-15C Programming ...............................

65

Section 6: Programming Basics ..................................

66

The Mechanics ...............................................................

66

Creating a Program .....................................................

66

Loading a Program ......................................................

66

Intermediate Program Stops ...........................................

68

Running a Program .......................................................

68

How to Enter Data ........................................................

69

Program Memory .........................................................

70

Further Information ..........................................................

74

Program Instructions .....................................................

74

Instruction Coding ........................................................

74

Memory Configuration ..................................................

75

Program Boundaries .....................................................

77

Unexpected Program Stops ...........................................

78

Abbreviated Key Sequences ..........................................

78

User Mode ..................................................................

79

Polynomial Expressions and Horner's Method ..................

79

Nonprogrammable Functions .........................................

80

Problems ........................................................................

81

Section 7: Program Editing ........................................

82

The Mechanics ...............................................................

82

Moving to a Line in Program Memory .............................

82

Deleting Program Lines .................................................

83

Inserting Program Lines .................................................

83

Examples .......................................................................

83

Further Information ..........................................................

85

Single-Step Operations .................................................

85

Line Position ................................................................

86

Insertions and Deletions ................................................

87

Initializing Calculator Status ..........................................

87

Problems ........................................................................

87

Section 8: Program Branching and Controls .................

90

The Mechanics ...............................................................

90

Branching ...................................................................

90

Conditional Tests ..........................................................

91

Contents 7

Flags ..........................................................................

92

Examples .......................................................................

93

Example: Branching and Looping ...................................

93

Example: Flags ............................................................

95

Further Information ..........................................................

97

GoTo ..........................................................................

97

Looping ......................................................................

98

Conditional Branching ..................................................

98

Flags ..........................................................................

98

The System Flags: Flags 8 and 9 ....................................

99

Section 9: Subroutines ...............................................

101

The Mechanics ...............................................................

101

GoTo Subroutine and Return ..........................................

101

Subroutine Limits ..........................................................

102

Examples .......................................................................

102

Further Information ..........................................................

105

The Subroutine Return ...................................................

105

Nested Subroutines ......................................................

105

Section 10: The Index Register and Loop Control ...........

106

The V and % Keys ....................................................

106

Direct Versus Indirect Data Storage With

The Index Register .....................................................

106

Indirect Program Control With the Index Register .............

107

Program Loop Control ...................................................

107

The Mechanics ...............................................................

107

Index Register Storage and Recall ..................................

107

Index Register Arithmetic ...............................................

108

Exchanging the X-Register .............................................

108

Indirect Branching With V .........................................

108

Indirect Flag Control With V ......................................

109

Indirect Display Format Control With V .......................

109

Loop Control with Counters: I and e ..................

109

Examples .......................................................................

111

Examples: Register Operations .......................................

111

Example: Loop Control With s .................................

112

Example: Display Format Control ....................................

114

Further Information ..........................................................

115

Index Register Contents .................................................

115

8 Contents

I and e ..........................................................

116

Indirect Display Control ...........................................

116

Part III: HP-15C Advanced Functions ....................

119

Section 11: Calculating With Complex Numbers ..........

120

The Complex Stack and Complex Mode ............................

120

Creating the Complex Stack ..........................................

120

Deactivating Complex Mode .........................................

121

Complex Numbers and the Stack ......................................

121

Entering Complex Numbers ...........................................

121

Stack Lift in Complex Mode ...........................................

124

Manipulating the Real and Imaginary Stacks ..................

124

Changing Signs ..........................................................

124

Clearing a Complex Number .......................................

125

Entering a Real Number ...............................................

128

Entering a Pure Imaginary Number ...............................

129

Storing and Recalling Complex Numbers .......................

130

Operations With Complex Numbers ................................

130

One-Number Functions ................................................

131

Two-Number Functions .................................................

131

Stack Manipulation Functions .......................................

131

Conditional Tests .........................................................

132

Complex Results from Real Numbers ..............................

133

Polar and Rectangular Coordinate Conversions .................

133

Problems .......................................................................

135

For Further Information ...................................................

137

Section 12: Calculating With Matrices ........................

138

Matrix Dimensions .........................................................

140

Dimensioning a Matrix .................................................

141

Displaying Matrix Dimensions .......................................

142

Changing Matrix Dimensions ........................................

142

Storing and Recalling Matrix Elements ..............................

143

Storing and Recalling All Elements in Order ...................

143

Checking and Changing Matrix Elements Individually .....

145

Storing a Number in All Elements of a Matrix .................

147

Matrix Operations .........................................................

147

Matrix Descriptors .......................................................

147

The Result Matrix .........................................................

148

Contents 9

Copying a Matrix .......................................................

149

One-Matrix Operations ................................................

149

Scalar Operations .......................................................

151

Arithmetic Operations ..................................................

153

Matrix Multiplication ...................................................

154

Solving the Equation AX = B ..........................................

156

Calculating the Residual ...............................................

159

Using Matrices in LU Form ............................................

160

Calculations With Complex Matrices ...............................

160

Storing the Elements of a Complex Matrix ......................

161

The Complex Transformations Between Z

P

and Z .............

164

Inverting a Complex Matrix ..........................................

165

Multiplying Complex Matrices ......................................

166

Solving the Complex Equation AX = B ............................

168

Miscellaneous Operations Involving Matrices .....................

173

Using a Matrix Element With Register Operations ............

173

Using Matrix Descriptors in the Index Register .................

173

Conditional Tests on Matrix Descriptors ..........................

174

Stack Operation for Matrix Calculations ............................

174

Using Matrix Operations in a Program ..............................

176

Summary of Matrix Functions ...........................................

177

For Further Information ....................................................

179

Section 13: Finding the Roots of an Equation ................

180

Using _ .................................................................

180

When No Root Is Found ..................................................

186

Choosing Initial Estimates ................................................

188

Using _ in a Program ..............................................

192

Restriction on the Use of _ .......................................

193

Memory Requirements .....................................................

193

For Further Information ....................................................

193

Section 14: Numerical Integration ..............................

194

Using f .......................................................................

194

Accuracy of f .............................................................

200

Using f in a Program ..................................................

203

Memory Requirements .....................................................

204

For Further Information ....................................................

204

10 Contents

Appendix A: Error Conditions ....................................

205

Appendix B: Stack Lift and the LAST X Register ...............

209

Digit Entry Termination ....................................................

209

Stack Lift ........................................................................

209

Disabling Operations ...................................................

210

Enabling Operations ....................................................

210

Neutral Operations ......................................................

211

LAST X Register ...............................................................

212

Appendix C: Memory Allocation ................................

213

The Memory Space .........................................................

213

Registers .....................................................................

213

Memory Status (W) ..................................................

215

Memory Reallocation ......................................................

215

The m % Function ................................................

215

Restrictions on Reallocation ...........................................

216

Program Memory ............................................................

217

Automatic Program Memory Reallocation ........................

217

Two-Byte Program Instructions .......................................

218

Memory Requirements for the Advanced Functions .............

218

Appendix D: A Detailed Look at _ ......................

220

How _ Works .......................................................

220

Accuracy of the Root .......................................................

222

Interpreting Results ..........................................................

226

Finding Several Roots ......................................................

233

Limiting the Estimation Time ..............................................

238

Counting Iterations .......................................................

239

Specifying a Tolerance .................................................

239

For Advanced Information ................................................

239

Appendix E: A Detailed Look at f ...........................

240

How f Works .............................................................

240

Accuracy, Uncertainty, and Calculation Time .....................

241

Uncertainty and the Display Format ...................................

245

Conditions That Could Cause Incorrect Results ....................

249

Conditions That Prolong Calculation Time ..........................

254

Obtaining the Current Approximation to an Integral ...........

257

For Advanced Information ................................................

258

Contents 11

Appendix F: Batteries .............................................

259

Low-Power Indication .......................................................

259

Installing New Batteries ................................................

259

Verifying Proper Operation (Self-Tests) ...............................

261

Function Summary and Index .....................................

262

Complex Functions ..........................................................

262

Conversions ...................................................................

262

Digit Entry ......................................................................

262

Display Control ..............................................................

263

Hyperbolic Functions .......................................................

263

Index Register Control .....................................................

263

Logarithmic and Exponential Functions ..............................

263

Mathematics ..................................................................

264

Matrix Functions .............................................................

264

Number Alteration ..........................................................

265

Percentage .....................................................................

266

Prefix Keys .....................................................................

266

Probability .....................................................................

266

Stack Manipulation .........................................................

266

Statistics ........................................................................

267

Storage .........................................................................

267

Trigonometry ..................................................................

268

Programming Summary and Index ..............................

269

Subject Index ...........................................................

271

12

The HP-15C:

A Problem Solver

The HP-15C Advanced Programmable Scientific Calculator is a powerful

problem solver, convenient to carry and easy to hold. Its continuous

memory retains data and program instructions indefinitely until you choose

to reset it. Though sophisticated, it requires no prior programming

experience or knowledge of programming languages to use it.

The new HP-15C is a modern re-release of the original HP-15C introduced

in 1982. While the battery life of the new version is now estimated to be 1

year for normal use, the calculator is now at least 150 times faster than the

original. The low-power indicator gives you plenty of warning before the

calculator stops functioning.

The HP-15C also conserves power by automatically shutting its display off

if it is left inactive for a few minutes. But don't worry about losing data 

any information contained in the HP-15C is saved by Continuous Memory.

A Quick Look at v

Your Hewlett-Packard calculator uses a unique operating logic, represented

by the v key, that differs from the logic in most other calculators.

You will find that using v makes nested and complicated

calculations easier and faster to work out. Let's get acquainted with how this

works.

For example, let's look at the arithmetic functions. First we have to get the

numbers into the machine. Is your calculator on? If not, press =. Is the

display cleared? To display all zeros, you can press | ` that is, press

|, then −.

*

To perform arithmetic, key in the first number, press v

to separate the first number from the second, then key in the second number

and press +, -, * or ÷. The result appears immediately after you

press any numerical function key.

*

If you have not used an HP calculator before, you will notice that most keys have three labels. To use the

primary function  the one printed in white on top of the key  just press that key. For those printed in gold

or blue, press the gold ´ key or the blue | key first.

The HP-15C: A Problem Solver 13

The display format used in this handbook is • 4 (the decimal point is

     

calculator does not show four decimal places, you may want to press

´• 4 to match the displays in the examples.

Manual Solutions

Run through the following two-number calculations. It is not necessary to

clear the calculator between problems. If you enter a digit incorrectly, press

− to undo the mistake, then key in the correct number.

To Compute

Keystrokes

Display

9 - 6 = 3

9 v 6 -

3.0000

9 × 6 = 54

9 v 6 *

54.0000

9 ÷ 6 = 1.5

9 v 6 ÷

1.5000

9

6

= 531,441

9 v 6 Y

531,441.0000

Notice that in the four examples:



Both numbers are in the calculator before you press the function key.



v is used only to separate two numbers that are keyed in one

after the other.



Pressing a numeric function key, in this case - * ÷ or Y,

executes the function immediately and displays the result.

To see the close relationship between manual and programmed problem

solving, let's first calculate the solution to a problem manually, that is, from

the keyboard. Then we'll use a program to calculate the solution to the same

problem with different data.

14 The HP-15C: A Problem Solver

The time an object takes to fall to the ground (ignoring air friction) is given

by the formula

g

2h

t 

,

where t = time in seconds,

h = height in meters,

g = the acceleration due to gravity,

9.8 m/s

2

.

Example: Compute the time taken by a

stone falling from the top of the Eiffel

Tower (300.51 meters high) to the earth.

Keystrokes

Display

300.51 v

300.5100

Enter h.

2 *

601.0200

Calculates 2h.

9.8 ÷

61.3286

(2h) /g.

¤

7.8313

Falling time, seconds.

Programmed Solutions

Suppose you wanted to calculate falling times from various heights. The

easiest way is to write a program to cover all the constant parts of a

calculation and provide for entry of variable data.

Writing the Program. The program is similar to the keystroke sequence

you used above. A label is useful to define the beginning of a program, and

a return is useful to mark the end of a program. Also, the program must

accommodate the entry of new data.

Loading the Program. You can load a program for the above problem by

pressing the following keys in sequence. (The display shows information

which you can ignore for now, though it will be useful later.)

The HP-15C: A Problem Solver 15

Keystrokes

Display

|¥

000-

Sets HP-15C to Program

mode. (PRGM

annunciator on.)

´ CLEAR M

000-

Clears program memory.

(This step is optional

here.)

´bA

001-42,21,11

Label "A" defines the

beginning of the

program.

2

002- 2

*

003- 20

9

004- 9

The same keys you

pressed to solve the

.

005- 48

problem manually.

8

006- 8

÷

007- 10

¤

008- 11

|n

009- 43 32



of the program.

|¥

7.8313

Switches to Run mode.

(No PRGM

annunciator.)

Running the Program. Enter the following information to run the

program.

Keystrokes

Display

300.51

Height of the Eiffel Tower.

´A

7.8313

Falling time you calculated

earlier.

1050 ´A

14.6385

The time (seconds) for a stone

to reach the ground after release

from a blimp 1050 m high.

16 The HP-15C: A Problem Solver

With this program loaded, you can quickly calculate the time of descent of

an object from different heights. Simply key in the height and press

´A. Find the time of descent for objects released from heights of

100 m, 2 m, 275 m, and 2,000 m.

The answers are: 4.5175 s; 0.6389 s; 7.4915 s; and 20.2031 s.

That program was relatively easy. You will see many more aspects and

details of programming in part II. For now, turn the page to take an in-depth

look at some of the calculator's important operating basics.

Part l

HP-15C

Fundamentals

18

Section 1

Getting Started

Power On and Off

The = key turns the HP-15C on and off.

*

To conserve power, the

calculator automatically turns itself off after a few minutes of inactivity.

Keyboard Operation

Primary and Alternate Functions

Most keys on your HP-15C perform one primary and two alternate, shifted

functions. The primary function of any key is indicated by the character(s)

on the face of the key. The alternate functions are indicated by the gold

characters printed above the key and the blue characters printed on the

lower face of the key.



To select the primary function printed on

the face of a key, press only that key. For

example: ÷.



To select the alternate function printed in

gold or blue, press the like-colored prefix

key (´ or |) followed by the function

key. For example: ´ _; |

£.

Throughout this handbook, we will observe certain conventions in referring

to alternate functions. References to the function itself will appear as just the

W the use of

the key will include the prefix key, such a | W

CLEAR

CLEAR, such as "the CLEAR Q 

´ CLEAR M

*

Note that the = key is lower than the other keys to help prevent its being pressed inadvertently.

Section 1: Getting Started 19

Notice that when you press the ´ or |

prefix key, an f or g annunciator appears

and remains in the display until a function

key is pressed to complete the sequence.

Prefix Keys

A prefix key is any key which must precede another key to complete the

key sequence for a function. Certain functions require two parts: a prefix

key and a digit or other key. For your reference, the prefix keys are:

"

^

•

G

f

>

i

O

m

´

|

P

I

l

F

T

s

?

t

H

b

<

_

X

If you make a mistake while keying in a prefix for a function, press ´

CLEAR u to cancel the error. The CLEAR u key is also used

to show the mantissa of a displayed number, so all 10 digits of the number

in the display will appear for a moment after the u key is pressed.

Changing Signs

Pressing “ (change sign) will change the sign (positive or negative) of

any displayed number. To key in a negative number, press “ after its

digits have been keyed in.

Keying in Exponents

‛ (enter exponent) is used when keying in a number with an exponent.

First key in the mantissa, then press ‛ and key in the exponent.

For a negative exponent press “ after keying in the exponent.

*

For

example, to key in Planck's constant (6.6262×10

-34

Joule-seconds) and

multiply it by 50:

*

“ may also be pressed after ‛ and before the exponent, with the same result (unlike the mantissa,

where digit entry must precede “).

0.0000

f

20 Section 1: Getting Started

Keystrokes

Display

6.6262

‛

6.6262 00

The 00 prompts you to

key in the exponent.

3

6.6262 03

(6.6262×10

3

).

4

6.6262 34

(6.6262×10

34

).

“

6.6262 -34

(6.6262×10

-34

).

v

6.6262 -34

Enters number.

50 *

3.3131 -32

Joule-seconds.

Note: Decimal digits from the mantissa that spill into the exponent

field will disappear from the display when you press , but will be

retained internally.

To prevent a misleading display pattern, ‛ will not operate with a

number having more than seven digits to the left of the radix mark (decimal

point), nor with a mantissa smaller than 0.000001. To key in such a number,

use a form having a greater exponent value (whether positive or negative).

For example, 123456789.8×10

23

can be keyed in as 1234567.898×10

25

;

0.00000025×10

-15

can be keyed in as 2.5×10

-22

.

The “CLEAR” Keys

Clearing means to replace a number with zero. The clearing operations in

the HP-15C are (the table is continued on the next page):

Clearing Sequence

Effect

|`

Clears display (X-register).

−

In Run mode:

Clears last digit or entire display.

In Program mode:

Deletes current instruction.

´ CLEAR ∑

Clears statistics storage registers, display,

and the memory stack (described in

section 3).

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